Question: What is the amplitude of $h(x)=7\sin\left(\dfrac{3\pi}{4} x-\dfrac{\pi}{4}\right)+6$ ?
Explanation: Amplitude in sinusoids of the form $f(x)=a\sin(bx+c)+d$ The amplitude of a sinusoid of the form $f(x)={a}\sin(bx + c) + d$ is equal to $|{a}|$. [How can we justify this given our graphical understanding of amplitude?] Finding the amplitude The amplitude of $h(x) = {7}\sin\left(\dfrac{3\pi}{4} x-\dfrac{\pi}{4}\right)+6$ is $|{7}|=7$.